1.

If `3^(x)+3^(y)=3^(x+y)` then what is `(dy)/(dx)` equal to?A. `(3^(x+y)-3^(x))/(3^(y))`B. `(3^(x-y)(3^(y)-1))/(1-3^(x))`C. `(3^(x)+3^(y))/(3^(x)-3^(y))`D. `(3^(x)+3^(y))/(1+e^(x+y)`

Answer» Correct Answer - B
`3^(x)+3^(y)=3^(x+y)`
On differentiating w.r.t., we get
`3^(x)log 3+3^(y)log3(dy)/(dx)=3^(x+y)log3(1+(dy)/(dx))`
`rArr" "log3[3^(x)+3^(y)(dy)/(dx)]=log3.3^(x+y)(1+(dy)/(dx))`
`rArr" "(dy)/(dx)(-3^(x+y)+3^(y))=3^(x+y)-3^(x)`
`=3^(x).3^(y)-3^(x)=3^(x)(3^(y)-1)`
`rArr" "(dy)/(dx)=(3^(x)(3^(y)-1))/(3^(y)(1-3^(x)))=(3^(x-y)(3^(y)-1))/((1-3^(x)))`


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